In a right triangle, one of the acute angles is twice as large as the other acute angle. Find the measure of the two acute angles.

Since we know that the sum of the angles of any triangle is 180 degrees, and a right angle measures 90 degrees, we can subtract 90 from 180 to get 120. We can then divide 120 by 3 which gives us 40. Since one acute angle is double the size of the other and we still have 80 degrees to place, and 80 is double 40, the answer is:

The smaller angle is 40 degrees and the larger angle is 80 degrees.